Transport Properties of a Dirty Two-Band Superconductor in the Mixed State nearHc2

Abstract

The mixed-state ultrasonic-attenuation and thermal-conductivity coefficients are obtained for a transition-metal superconductor containing a high concentration of nonmagnetic impurities. Expressing the transport coefficients as the sums of correlation functions of the individual bands, the attenuation and thermal-conductivity coefficients are obtained by the use of an equivalence theorem due to Maki. The resulting two-band expressions exhibit the linear field dependences observed in dirty transition-metal superconductors in the gapless state near $H_{c2\mathrm{}}$. The two-band mixed-state thermal-conductivity coefficient for a dirty superconductor is then used qualitatively to show why the slope of the normalized thermal conductivity minus 1 versus the applied field for two dirty transition-metal superconductors (${\mathrm{Nb}}_{80}$ ${\mathrm{Mo}}_{20}$ and ${\mathrm{Nb}}_{85}$ ${\mathrm{Mo}}_{15}$) having only slightly different $\frac{l}{{\xi }_0}$ ratios agrees with the one-band mixed-state thermal-conductivity expression of Caroli and Cyrot for the case of the dirtier ${\mathrm{Nb}}_{80}$ ${\mathrm{Mo}}_{20}$ specimen, while for the case of the ${\mathrm{Nb}}_{85}$ ${\mathrm{Mo}}_{15}$ specimen the slope is much greater than that predicted by the one-band expression.